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A guide through the hidden world of mathematics.

When mathematicians speak of maths they speak of a wondrous land of beauty, elegance, order and precision, a place where dreams are quantified and bold new concepts can be proven long before they can be observed.

Fortunately for those of us lacking the skills to navigate it, along comes Alex Bellos, an enthusiastic guide to show us the way.

As every mathematically ungifted school child knows, few teachers have the ability to explain the world of maths. While they may describe concepts and procedures well enough to pass an exam, the underlying beauty of the ideas, the precision of the language and even the philosophy of the subject remain, for most, elusive.

Bellos is not like that. He has an uncanny knack for making us feel we are discovering this foreign land with the early explorers. A truly gifted science communicator, one reviewer compared him to Martin Gardner, the prolific popular maths and science writer whose columns in Scientific American delighted a generation (see COSMOS 55, page 106).

Alex through the Looking-Glass is the sequel to Bellos’ lighthearted history of maths, Adventures In Numberland. That book looked at the development of key concepts and the intimate relationship of numbers to the development of mankind. Through the Looking-Glass continues the journey, with further insights into the complex cultural relationships we have with numbers.

Along the way we learn wonderful new facts great and small, such as Shakespeare was the first to coin the name odd number. Who knew?

Earlier this year, Bellos, through his blog on The Guardian website, ran a global survey to find the world’s favourite number. He sifted through 30,000 responses to find the answer (7). The book revisits that idea, and opens by asking why we prefer some numbers to others. While pondering why 7 is such a popular number, he asks, is it significant that it is the number days of the week, of dwarves and of seas?

He looks at why we consider some numbers superstitious - how Belphegor, one of the seven princes of hell, gave his name to a prime number containing a 666 and what is it about 13?

But serious maths seekers should not be put off by this frivolity, as Bellos soon enters more demanding territory – from triangles, rotations and power laws, to fractals, cones and curves.

In the chapters on pure maths the going gets tougher, but it is still enjoyable. We explore Greek geometry, how the triangle led to the cone that led to the curves that could describe the movement of the planets; the maths behind the rotation of a wheel, the swing of the pendulum and the bounce of the spring. Calculus gets its own chapter that takes in everything from the dispute between Newton and Liebniz about who first invented it, to how it works and what it means.

All is delivered with a good helping of intriguing stories, anecdotes and beautiful illustrations.